Download 5.1,2 Work and Energy Theorem. Work has different meaning in physics.

Ch5 Energy
5.1,2 Work and Energy Theorem.
Work has different meaning in physics.
Definition:
work is proportional to the mass and the square total energy of the system remains the same at
of the speed. This is definition of the kinetic
all time.
energy.
Conservative force:
1
W  Fd cos
KE  mv 2
1.Conservative force keeps the total energy of a
 
2
system constant at all time. It only transforms
 F d
Then, work-energy theorem can be deduced
the energy from one form(i.e potential energy)

F
from the definition of work.
to the other forms(i.e. Kinetic energy).

2. the work it does moving an object between

Wnet  KE
two points is the same no matter what path is
d
Work doesn’t happen by itself. Work is done by This implies that net work changes kinetic
taken.
something on the object of interest.
energy of the object of interest.
 W2
Work is a scalar quantity.
W2
SI unit is J (joule)
Here we used equation of motion under a
W1
W1
The U.S. customary unit is the foot-pound.
constant acceleration to derive work-energy
Work can be positive or negative.
theorem. But this is a valid under all
W1  W2
If a force and a displacement are in opposite
circumstances and if we use calculus, we can
If work done by a force is different in the two
directions, work is negative.
derive the theorem for the case of a variable
different paths shown above(left diagram),
If a force and a displacement are perpendicular force as well.
Energy is not conserved in the closed
to each other, work is zero.
system(right diagram).
If a force and a displacement are in the same 5.3 Gravitational Potential Energy.
3. All fundamental forces are conservative
direction, work is positive.
Work done by gravity.
forces. Also spring force is conservative.
Wg  mg ( y f  yi )
Now from the definition of work, lets use some When we define upward is positive direction, Nonconservative force:
tricks
then from the work-energy theorem,
1.generally dissipative.
2.the work is path dependent.
Wnet  mg ( y f  yi )  KE
Wnet  Fnet x
3. friction and external force by a person are
2
2
examples of nonconservative force.
( KE f  KEi )  mg ( y f  yi )  0
v  v0
 (ma )(
)
Strictly speaking, all forces are conservative.
2a
from this equation we can deduce that PE  mgy
However, the nonconservative force transforms
1
1
Finally
 mv 2  mv02
energy to a form that is hard to measure. So, we
2
2
KEi  PEi  KE f  PE f
can not keep track of the energy transfer due to
When work is done on a object, the speed is
Thus, in any isolated system of objects
the nonconservative forces.
changing. The equation above shows that the interacting only through gravitational force, the
5.4 Spring Potential Energy
Spring force is also a conservative force.
According to Hooke’s law,
Fx  kx
Where k is spring constant and its unit is N/m
5.6 Power
Power: rate at which energy is transferred.
Average power: P 
W
 Fv
t
Instantaneous Power: P  Fv
The work done by the spring force is
1
Ws   kx 2
2
1
Ws   k ( x 2f  xi2 )
2
 KE
From this equation,
1
PE  kx2
2
When we include gravitational force and
nonconservative force to the equation,
Wnc  Wg  Ws  KE
Wnc  ( KE f  KEi )  ( PE gf  PE gi )  ( PE sf  PE si )
This is the key equation we will use in this
chapter.
This is the equation of the conservation of
mechanical energy.
At this point, we can now know that work
transfers energy from one object to the other
object.
SI unit W(watt)
Unit in the US horsepower(hp)
1hp = 746 W
5.7 Work done by a varying force.
Area under F vs. x curve is the work done by the
force.
An Eskimo returning from a successful fishing trip
pulls a sled loaded with salmon. The total mass of A 1.00 x103-kg elevator car carries a maximum load of
the sled and salmon is 50.0 kg and the Eskimo
8.00 x 102 kg. A constant frictional force of 4.00 x
exerts a force of magnitude 1.20 x 102 N on the
103 N retards its motion upward. What minimum
sled by pulling on the rope. How much work does
power, in kilowatts and in horsepower, must the
he do on the sled if θ=30.0° and he pulls the sled
motor deliver to lift the fully loaded elevator car
5.00 m
at a constant speed of 3.00 m/s?
A 0.500 kg block rests on a horizontal, frictionless
surface as in the figure below. The block is
pressed back against a spring having a constant of
k=625 N/m, compressing the spring by 10.0 cm to
point A. Then the block is released. (a) find the
maximum distance d the block travels up the
frictionless incline if θ=30.0°. (b) how fast is the
block going at half its maximum height?